How to create a SparseArray satisfying multiple conditions on Parts and Elements of a Matrix?

Question

I have a matrix m1 of size $3 \times 19$.

Rows $1$, $2$ and $3$ represent $3$ different groups, and columns represent $4$ different blocks:

1. block1 - columns $1$, $2$, and $3$,
2. block2 - columns $4$, $5$, $6$, $7$, and $8$,
3. block3 - columns $9$, $10$, $11$, and $12$,
4. block4 - columns $13$--$19$.

I want to construct a SparseArray, of the size $3 \times 19$, such that if any of the matrix m1 elements is less than for example $5000$, then all of the elements of the corresponding group and block should be equal to $1$. If all of the elements of the corresponding group and block are greater than $5000$, then the values of the SparseArray should be equal to $0$.

This is my input matrix m1:

    m1 = {{17000, 14542, 17000, 7000, 7000, 7000, 7000, 5666, 5127, 3810, 
       6027, 7000, 12000, 12000, 12000, 12000, 12000, 17000, 
       12000}, {17000, 12070, 17000, 7000, 7000, 7000, 7000, 5100, 4435, 
       3010, 5575, 7000, 12000, 12000, 12000, 12000, 12000, 17000, 
       12000}, {17000, 9743, 17000, 7000, 7000, 7000, 5530, 4250, 4358, 
       2876, 5002, 7000, 12000, 12000, 12000, 12000, 12000, 17000, 12000}}

I use Map and Boole to generate matrix m2:

    m2 = Boole[Map[# < 5000 &, m1, {2}]]

This is the output for m2:

(* {{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
    {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
    {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}} *)

Then I need to specify the conditions for my final solution.

    solution=Normal[SparseArray[{
         {i_, j_} /; i == 1 && 1 <= j <= 3 && Total[m2[[1, 1 ;; 3]]] >= 1 -> 1, 
         {i_, j_} /; i == 1 && 4 <= j <= 8 && Total[m2[[1, 4 ;; 8]]] >= 1 -> 1, 
         {i_, j_} /; i == 1 && 9 <= j <= 12 && Total[m2[[1, 9 ;; 12]]] >= 1 -> 1,
         {i_, j_} /; i == 1 && 13 <= j <= 19 && Total[m2[[1, 13 ;; 19]]] >= 1 -> 1, 
         {i_, j_} /; i == 2 && 1 <= j <= 3 && Total[m2[[2, 1 ;; 3]]] >= 1 -> 1, 
         {i_, j_} /; i == 2 && 4 <= j <= 8 && Total[m2[[2, 4 ;; 8]]] >= 1 -> 1,
         {i_, j_} /; i == 2 && 9 <= j <= 12 && Total[m2[[2, 9 ;; 12]]] >= 1 -> 1,
         {i_, j_} /; i == 2 && 13 <= j <= 19 && Total[m2[[2, 13 ;; 19]]] >= 1 -> 1, 
         {i_, j_} /; i == 3 && 1 <= j <= 3 && Total[m2[[3, 1 ;; 3]]] >= 1 -> 1,
         {i_, j_} /; i == 3 && 4 <= j <= 8 && Total[m2[[3, 4 ;; 8]]] >= 1 -> 1,
         {i_, j_} /; i == 3 && 9 <= j <= 12 && Total[m2[[3, 9 ;; 12]]] >= 1 -> 1,
         {i_, j_} /; i == 3 && 13 <= j <= 19 && Total[m2[[3, 13 ;; 19]]] >= 1 -> 1,
         Dimensions[m2]]]

This is the result I wanted:

(* {{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, 
    {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, 
    {0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}} *)

I believe that there is a better way to get the results I need.

Answer 1

Edit

I enjoy using image functions for solving non-imaging problems. Here is a way:

row = Flatten[Block[{i = 0}, ConstantArray[++i, #] & /@ {3, 5, 4, 7}]];
a = {row, row + Max@row, row + 2 Max@row};     (* It's a "morphological view" of m1*)
f[m_] := Unitize[Floor[a /. ComponentMeasurements[{a, Image[m1/5000]}, "Min", # < 1 &]]] - 1 // Abs
f[m1]
(*
{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, 
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, 
 {0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}}
*)

**Old incarnation **

(* Create matrix "a" components according to your Blocks defs *)
row = Flatten[Block[{i = 0}, ConstantArray[++i, #] & /@ {3, 5, 4, 7}]];
a = {row, row + Max@row, row + 2 Max@row};
ArrayPlot[a, ColorFunction -> "Rainbow"]

(* Build a vector "rep" with one binary byte for each block in matrix "a" *)
rep = Boole[# < 5000] & /@ (Extract[m, #] & /@ Position[a, #] & /@ 
      Range@Max@a) /. x : {_Integer ..} :> Min[x];

(* Replace each block value for its corresponding spec *)
b = a /. Thread[Range@Max@a -> rep]
ArrayPlot[b, ColorFunction -> "Rainbow"]

(*
{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, 
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, 
 {0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}}
*)